# Algebra

Learn about functions, graphs, lines, and polynomials. "Algebra" is the math for describing how different things are related.

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1. Addition and subtraction

Locating integers and non-integers on the number line

Using the number line to add numbers

Moving left on the number line

What happens when you add negative numbers?

Turns out it's addition!

The "size" of a number, or how far it is from zero

Ways to find the distance between any two numbers

2. Multiplication and division

Multiplying positive numbers, in any order

Discover what happens when you multiply by 1 and 0

Dividing positive numbers, and ways to think about it

An operation you just can't perform...

Is there more than one way to evaluate an expression?

Getting rid of parentheses when you add and multiply

What happens when you multiply negatives together?

What happens when you divide negative numbers?

Distributing a negative flips the signs

What to do when you have too many parentheses!

Discover how to find the "average" of numbers

3. Factoring

Dividing by a factor always gives you a whole number

Their only factors are 1 and themselves

Pulling out common factors using the distributive law

Flip the signs when you factor out negative numbers

The biggest factor that numbers have in common

When two numbers have no common factors

A 2000-year-old way to calculate the GCF

What you get when you multiply numbers by integers

The smallest multiple numbers have in common

4. Fractions

Draw and compare fractions, and convert to decimals

What's 1/2 times 3/5? Learn the trick in this lesson!

How to tell when fractions are equal or which is bigger

Simplifying fractions by removing common factors

Add and subtract fractions using common denominators

Dividing by a fraction is really multiplying by its reciprocal!

A number's multiplicative inverse is 1 over the number

Switching between mixed and improper fractions

The distributive law works for multiplying, but also dividing

Evaluating fractions of numbers (like 5/7 of 210)

5. Powers and roots

Multiplying a number by itself

Squaring, cubing, raising to the fourth, and so on...

Work backwards to find the number that was squared

How to find the roots of numbers that are NOT square

Do negative numbers even have square roots?

Cube roots, fourth roots, fifth roots, and so on...

Order of operations, now with exponents!

6. Rules for powers

A rule for multiplying one power by another

A rule for dividing one power by another

A rule for raising one power to another

It works for multiplication and division, but that's it!

What happens when you raise a number to the zero?

What does it mean to raise to a NEGATIVE exponent?

Taking a root is really the same as raising to a power

What does it mean to raise to the 2/3 power?

Roots are also exponents, so the same rules apply!

Getting smaller numbers under the root

7. Solving equations

Solve for unknown values using the number line

Learn how to evaluate expressions with variables

Adding or subtracting on both sides of equations

Multiplying or dividing on both sides of equations

A quick way to solve equations with fractions

Numbers in front of variables

Adding/subtracting terms with matching variables

Sometimes it takes more than one step to solve!

Solving equations when they have more than one variable

Some equations have no solutions, others have plenty!

8. Inequalities and simultaneous equations

Plotting inequalities on the number line

Solving and plotting multi-step inequalities

What happens when you multiply by a negative

Solve for both variables when you have two equations

Sometimes two equations have no solutions, or many!

9. Coordinates

Plotting points and finding their coordinates

The four quadrants, and the coordinates they contain

Given two points, which point is exactly halfway between?

10. Slope

A number that tells you the steepness of a line

How to calculate the slope between any two points

Discover what it means when slope is negative

What are the slopes of horizontal and vertical lines?

Two steps that will always give you the correct slope

Explore why parallel lines have the same slope

Discover how slopes of perpendicular lines relate

11. Lines

Turn an equation into your very first graph!

Turning an equation into a line, and vice versa

A formula for when you know the slope and coordinates

Forget equations, let's just look at the graphs!

Figuring out where lines cross the x- and y-axes

Given two lines, can you determine where they cross?

Exploring a graph that's not a line

Simplify inequalities with two variables and test solutions

Graph inequalities on the coordinate plane

12. Polynomials

Learn about a common type of algebraic expression

Computing sums and differences of polynomials

Multiply and divide polynomials with one term

Multiply binomials together using FOIL

How to multiply polynomials with many terms

A neat trick for simplifying certain binomials

13. Quadratics

Sometimes, equations can have two solutions

Plot points to draw your very first parabola

Every quadratic graph boils down to these 3 numbers

An extremely useful trick for solving some equations

A method for solving ANY quadratic equation!

A quick way to tell how many solutions a quadratic has

14. Functions

15. Polynomials